相关论文: 6j-symbols for symmetric representations of SO(n) …
The expressions of the coupling coefficients (3j-symbols) for the most degenerate (symmetric) representations of the orthogonal groups SO(n) in a canonical basis (with SO(n) restricted to SO(n-1)) and different semicanonical or tree bases…
The coupling coefficients (3j-symbols) for the symmetric (most degenerate) irreducible representations of the orthogonal groups SO(n) in a canonical basis and different semicanonical (tree) bases [with SO(n) restricted to SO(n')\times…
We study 6j-symbols, or Racah coefficients for tensor products of infinite-dimensional unitary principal series representations of the group SL(2,C). These symbols were constructed earlier by Ismagilov and we rederive his result (up to some…
We show that the complex hypergeometric function describing $6j$-symbols for $SL(2,\mathbb{C})$ group is a special degeneration of the $V$-function -- an elliptic analogue of the Euler-Gauss $_2F_1$ hypergeometric function. For this…
In this paper we derive new symmetry and new expression for $6j$-symbols of the unitary principal series representations of the $SL(2,\mathbb{C})$ group. This allowed us to derive for them the analogue of the Regge symmetry.
Explicit expressions are found for the $6j$ symbols in symmetric representations of quantum $\mathfrak{su}_N$ through appropriate hypergeometric Askey-Wilson (q-Racah) polynomials. This generalizes the well-known classical formulas for…
We present explicit closed-form expressions for the general group-theoretical factor appearing in the alpha-topology of a high-temperature expansion of SO(n)-symmetric lattice models. This object, which is closely related to 6j-symbols for…
A well known recurrence relation for the 6j-symbol of the quantum group su_q(2) is realized as a tridiagonal, symmetric eigenvalue problem. This formulation can be used to implement an efficient numerical evaluation algorithm, taking…
We will attach a scalar invariant to a tetrahedron whose edges are labelled by irreducible representations of a ternary orthogonal group $\mathrm{SO}_3$ over a local field. This generalizes the $6j$ symbol whose theory was developed by…
We revisit the definition of the 6j-symbols from the modular double of U_q(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral…
The 6j-symbol is a fundamental object from the re-coupling theory of SU(2) representations. In the limit of large angular momenta, its asymptotics is known to be described by the geometry of a tetrahedron with quantized lengths. This…
Seven different triple sum formulas for $9j$ coefficients of the quantum algebra $u_q(2)$ are derived, using for these purposes the usual expansion of $q$-$9j$ coefficients in terms of $q$-$6j$ coefficients and recent summation formula of…
We show that general $3n-j (n>2)$ symbols of the first kind and the second kind for the group SU(2) can be reformulated in terms of binomial coefficients. The proof is based on the graphical technique established by Yutsis, et al. and…
It is shown that the well known Racah sum rule and Biedenharn-Elliott identity satisfied by the recoupling coefficients or by the $6-j$ symbols of the usual rotation $SO(3)$ algebra can be extended to the corresponding features of the…
Recent interest in the Kashaev-Murakami-Murakami hyperbolic volume conjecture has made it seem important to be able to understand the asymptotic behaviour of certain special functions arising from representation theory -- for example, of…
For q a root of unity of order 2r, we give explicit formulas of a family of 3-variable Laurent polynomials J_{i,j,k} with coefficients in Z[q] that encode the 6j-symbols associated with nilpotent representations of U_qsl_2. For a given…
We study the $6j$ symbol for the conformal group, and its appearance in three seemingly unrelated contexts: the SYK model, conformal representation theory, and perturbative amplitudes in AdS. The contribution of the planar Feynman diagrams…
In the paper an explicit formula for an arbitrary $6j$-symbol for finite-dimensional irreducible representations of the algebra $\mathfrak{gl}_3$ is derived. A $6j$-symbol is written as a result of substitution of $\pm 1$ into a series of…
This paper investigates the relation between colored HOMFLY-PT and Kauffman homology, $\text{SO}(N)$ quantum $6j$-symbols and $(a,t)$-deformed $F_K$. First, we present a simple rule of grading change which allows us to obtain the…
An explicit description of the multiplicity space that describes occurrences of irreducible representations in a splitting of a tensor product of two irreducible representations of $\mathfrak{gl}_n$ is given. Using this description an…